Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing

DOI10.1023/A:1012967211737zbMath1005.37028OpenAlexW280778890MaRDI QIDQ5957844

Konstantin Mischaikow, Hiroe Oka, Hiroshi Kokubu, Tomáš Gedeon

Publication date: 13 March 2002

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1012967211737

zbMATH Keywords

chaotic dynamics Conley index theory fast-slow systems slowly varying Hamiltonian systems symbolic coding

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Symbolic dynamics (37B10)

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Sloshing of a layered fluid with a free surface as a Hamiltonian system ⋮ Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in two dimensions ⋮ High-energy solutions for a phase transition problem. ⋮ Complex dynamics in one-dimensional nonlinear Schrödinger equations with stepwise potential ⋮ Three-dimensional sloshing: A consistent finite element approach ⋮ High frequency solutions for the singularly-perturbed one-dimensional nonlinear Schrödinger equation ⋮ Solutions of slowly and periodically varying differential equations. Applications to some classical examples ⋮ Clustering layers and boundary layers in spatially inhomogeneous phase transition problems.

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